Remark 2.2 Quasi-compactness has strong implications to the spectral properties of \(M\) . In particular, this is equivalent to the essential spectral radius \(r_{\text{ess}}(M)\)  being strictly less than \(r(M)\) . Since it is not central to our arguments, we do not define \(r_{\text{ess}}(M)\)  here and refer the reader to [1]}, [2]}, [3]} instead. This observation also implies that outside the essential spectral radius, there are at most finitely many other elements of \(\sigma (M)\) , each being an eigenvalue with finite-dimensional (generalised) eigenspace; see [4]}.

